Editing Singlet state (section)

== History ==
Singlets and the related [[Spin (physics)|spin]] concepts of [[Doublet state|doublets]] and [[Triplet state|triplets]] occur frequently in [[atomic physics]] and [[nuclear physics]], where one often needs to determine the total spin of a collection of particles. Since the only observed fundamental particle with zero spin is the extremely inaccessible [[Higgs boson]], singlets in everyday physics are necessarily composed of sets of particles whose individual spins are non-zero, e.g. {{sfrac|1|2}} or 1.

The origin of the term "singlet" is that bound quantum systems with zero net angular momentum emit photons within a single spectral line, as opposed to double lines ([[doublet state]]) or triple lines ([[triplet state]]).<ref>{{cite book |author-link=David Griffiths (physicist) |first=D.J. |last=Griffiths |title=Introduction to Quantum Mechanics |url=https://archive.org/details/introductiontoqu00grif_200 |url-access=limited |publisher=Prentice Hall |year=1995 |page=[https://archive.org/details/introductiontoqu00grif_200/page/n178 165]|isbn=9780131244054 }}</ref> The number of spectral lines <math>n</math> in this singlet-style terminology has a simple relationship to the spin quantum number: <math>n=2s+1</math>, and <math>s=(n-1)/2</math>.

Singlet-style terminology is also used for systems whose mathematical properties are similar or identical to angular momentum spin states, even when traditional spin is not involved. In particular, the concept of [[isospin]] was developed early in the history of particle physics to address the remarkable similarities of [[proton]]s and [[neutron]]s. Within [[Atomic nucleus|atomic nuclei]], protons and neutrons behave in many ways as if they were a single type of particle, the nucleon, with two states. The proton-neutron pair thus by analogy was referred to as a doublet, and the hypothesized underlying nucleon was assigned a spin-like doublet quantum number <math>I_3=\tfrac{1}{2}</math> to differentiate between those two states. Thus the neutron became a nucleon with isospin <math>I_3(n)=-\tfrac{1}{2}</math>, and the proton a nucleon with <math>I_3(p)=+\tfrac{1}{2}</math>. The isospin doublet notably shares the same [[Special unitary group|SU(2)]] mathematical structure as the <math>s=\tfrac{1}{2}</math> angular momentum doublet. It should be mentioned that this early particle physics focus on nucleons was subsequently replaced by the more fundamental [[quark]] model, in which protons and neutrons are interpreted as bound systems of three quarks each. The isospin analogy also applies to quarks, and is the source of the names [[Quark#Etymology|up]] (as in "isospin up") and [[Quark#Etymology|down]] (as in "isospin down") for the quarks found in protons and neutrons.

While for angular momentum states the singlet-style terminology is seldom used beyond triplets (spin=1), it has proven historically useful for describing much larger particle groups and subgroups that share certain features and are distinguished from each other by [[quantum number]]s beyond spin. An example of this broader use of singlet-style terminology is the nine-member "nonet" of the [[pseudoscalar meson]]s.